U.S. patent number 9,091,781 [Application Number 12/996,498] was granted by the patent office on 2015-07-28 for method for estimating formation permeability using time lapse measurements.
This patent grant is currently assigned to Schlumberger Technology Corporation. The grantee listed for this patent is Raphael Altman, Carlos Maeso, John C. Rasmus. Invention is credited to Raphael Altman, Carlos Maeso, John C. Rasmus.
United States Patent |
9,091,781 |
Altman , et al. |
July 28, 2015 |
Method for estimating formation permeability using time lapse
measurements
Abstract
A method for determining permeability of a subsurface formation
includes measuring a parameter related to fluid content of the
formation at a first time from within a wellbore penetrating the
formation. A rate of entry of fluid from the wellbore into the
formation is determined from the measurement of the parameter made
at the first time. The permeability is determined from the rate of
entry.
Inventors: |
Altman; Raphael (Houston,
TX), Rasmus; John C. (Richmond, TX), Maeso; Carlos
(Purtajaya, MY) |
Applicant: |
Name |
City |
State |
Country |
Type |
Altman; Raphael
Rasmus; John C.
Maeso; Carlos |
Houston
Richmond
Purtajaya |
TX
TX
N/A |
US
US
MY |
|
|
Assignee: |
Schlumberger Technology
Corporation (Sugar Land, TX)
|
Family
ID: |
41445191 |
Appl.
No.: |
12/996,498 |
Filed: |
June 3, 2009 |
PCT
Filed: |
June 03, 2009 |
PCT No.: |
PCT/US2009/046153 |
371(c)(1),(2),(4) Date: |
April 11, 2011 |
PCT
Pub. No.: |
WO2009/158160 |
PCT
Pub. Date: |
December 30, 2009 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20110184711 A1 |
Jul 28, 2011 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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61075678 |
Jun 25, 2008 |
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61110631 |
Nov 3, 2008 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01V
3/20 (20130101); G06F 30/00 (20200101); G01V
99/005 (20130101); E21B 49/005 (20130101); E21B
47/024 (20130101) |
Current International
Class: |
G06F
17/50 (20060101); E21B 47/024 (20060101); G01V
3/20 (20060101); G01V 3/00 (20060101); G01V
3/18 (20060101); E21B 21/08 (20060101); E21B
47/10 (20120101); E21B 49/00 (20060101); G01V
99/00 (20090101); G06G 7/58 (20060101) |
Field of
Search: |
;703/1,10
;73/152.05,152.18,152.21,152.29 ;324/325,356 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Allen, et al., "Invasion Revisited", Oilfield Review, Jul. 1991,
pp. 10-23. cited by applicant .
Alpak, et al., "Joint Inversion of Pressure and Time-Lapse
Electromagnetic Logging Measurements", SPWLA 44th Annual Logging
Symposium, Jun. 22-25, 2003. cited by applicant .
Alpak, et al., "Numerical Simulation of Mud-Filtrate Invasion in
Horizontal Wells and Sensitivity Analysis of Array Induction
Tools", SPWLA 43rd Annual Logging Symposium, Jun. 2-5, 2002. cited
by applicant .
Cannon, et al., "Interpretation of Asymmetrically Invaded
Formations with Azimuthal and Radial LWD Data", SPWLA 40th Annual
Logging Symposium, 1999. cited by applicant .
Li, et al., "A Novel Inversion Method for Interpretation of a
Focused MultiSensor LWD Laterolog Resistivity Tool", SPWLA 40th
Annual Logging Symposium, May 30-Jun. 3, 1999. cited by applicant
.
Malik, et al., "Influence of Petrophysical and Fluid Properties on
Array-Induction Measurements Acquired in the Presence of Oil-Based
Mud-Filtrate Invasion", SPWLA 48th Annual Logging Symposium, Jun.
3-6, 2007. cited by applicant .
Salazar, et al., "Automatic Estimation of Permeability From Array
Induction Measurements: Applications to Field Data", SPWLA 46th
Annual Logging Symposium, Jun. 26-29, 2005. cited by applicant
.
Semmelbeck, et al., "Invasion-Based Method for Estimating
Permeability from Logs", SPE Annual Technical Conference and
Exhibition, Oct. 22-25, 1995. cited by applicant .
Wu, et al., "Numerical Simulation of Mud-Filtrate Invasion in
Deviated Wells", SPE 87919--SPE Reservoir Evaluation &
Engineering, Apr. 2004, pp. 143-154. cited by applicant .
Yao, et al., "Reservoir Permeability Estimation From Time-Lapse Log
Data", SPE 25513--Spe Production Operations Symposium, Oklahoma
City, Mar. 21-23, 1993. cited by applicant .
International Search Report and Written Opinion issued in
PCT/US2009/048153 on Nov. 30, 2009, 5 pages. cited by applicant
.
Mexican Office Action for Mexican Patent Application No.
MX/a/2010/01114 dated Jan. 15, 2013. cited by applicant.
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Primary Examiner: Rivas; Omar Fernandez
Assistant Examiner: Calle; Angel
Attorney, Agent or Firm: Vereb; John Ballew; Kimberly
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATIONS
Priority is claimed from U.S. Provisional Application No.
61/075,678 filed on Jun. 25, 2008 and U.S. Provisional Application
No. 61/110,631 filed on Nov. 3, 2008.
Claims
What is claimed is:
1. A method for determining permeability of a subsurface formation,
comprising: measuring a parameter related to fluid content of the
formation at a first time from within a wellbore penetrating the
formation and at a second time later than the first time; in a
computer, determining a rate of entry of fluid from the wellbore
into the formation from the measurement of the parameter made at
the first time, wherein determining the rate of entry of the fluid
from the wellbore into the formation comprises: determining a first
lateral depth of invasion of the fluid from the wellbore by
inverting the parameter measurements made at the first time;
determining a second lateral depth of invasion by inverting the
parameter measurements made at the second time; and calculating a
fluid volume at the first and second times from the respective
lateral depths of invasion; and in the computer, determining
permeability from the rate of entry.
2. The method of claim 1 wherein the parameter comprises electrical
resistivity measurements having a plurality of different lateral
depths of investigation.
3. The method of claim 1 further comprising determining a volume of
fluid invasion at the first and second times from the respective
lateral depths of invasion.
4. The method of claim 1 wherein the first time is during a
continuous drilling operation following initial penetration of the
formation by a drill bit.
5. The method of claim 1 wherein the second time is during an
operating subsequent to a continuous drilling operation following
initial penetration of the formation by a drill bit.
6. The method of claim 5 wherein the subsequent operation comprises
at least one of backreaming, washing, inserting a drill string into
the wellbore and removing the drill string from the wellbore.
7. The method of claim 1 wherein the parameter measurements are
allocated to a rotary orientation of an instrument at a time of
measurement.
8. The method of claim 1 further comprising: in the computer
initializing a model of the subsurface formation into a reservoir
simulation program; in the computer adjusting at least one of a
differential pressure and a permeability in the initialized model
until a simulated fluid entry rate from the simulation program
substantially matches the fluid entry rate determined from the
measurements made at the first and second times.
9. The method of claim 8 further comprising estimating permeability
anisotropy in the computer from the reservoir simulation
program.
10. The method of claim 1 wherein the fluid in the wellbore is
water based.
11. The method of claim 1 wherein the fluid in the wellbore is oil
based.
12. A non-transitory computer-readable medium having computer
executable instructions that cause a computer to perform the steps
of: reading a measurement of a parameter related to fluid content
of a subsurface rock formation made at a first time from within a
wellbore penetrating the formation; reading a measurement of the
parameter made at a second time after the first time; determining a
rate of entry of fluid from the wellbore into the formation from
the measurements of the parameter made at the first time and at the
second time by: determining a first lateral depth of invasion of
the fluid from the wellbore by inverting the parameter measurements
made at the first time; determining a second lateral depth of
invasion by inverting measurements of the parameter made at the
second time; and calculating a fluid volume at the first and second
times from the respective first and second lateral depths of
invasion; and determining permeability from the rate of entry.
13. The non-transitory computer-readable medium of claim 12 wherein
the parameter comprises electrical resistivity measurements having
a plurality of different lateral depths of investigation.
14. The non-transitory computer-readable medium of claim 12,
wherein the computer executable instructions further cause the
computer to perform the step of determining a volume of fluid
invasion at the first and second times from the respective lateral
depths of invasion.
15. The non-transitory computer-readable medium of claim 12 wherein
the first time is during a continuous drilling operation following
initial penetration of the formation by a drill bit.
16. The non-transitory computer-readable medium of claim 12 wherein
the second time is during an operating subsequent to a continuous
drilling operation following initial penetration of the formation
by a drill bit.
17. The non-transitory computer-readable medium claim 16 wherein
the subsequent operation comprises at least one of backreaming,
washing, inserting a drill string into the wellbore and removing
the drill string from the wellbore.
18. The non-transitory computer-readable medium of claim 12 wherein
the parameter measurements are allocated to a rotary orientation of
an instrument at a time of measurement.
19. The non-transitory computer-readable medium of claim 12 wherein
the computer executable instructions further cause the computer to
perform steps of: initializing a model of the subsurface formation
into a reservoir simulation program; and adjusting at least one of
a differential pressure and a permeability in the initialized model
until a simulated fluid entry rate from the simulation program
substantially matches the fluid entry rate determined from the
measurements made at the first and second times.
20. The non-transitory computer-readable medium of claim 12 wherein
the computer executable instructions further cause the computer to
estimate permeability anisotropy from the reservoir simulation
program.
21. The non-transitory computer-readable medium of claim 12 wherein
the fluid in the wellbore is water based.
22. The non-transitory computer-readable medium of claim 12 wherein
the fluid in the wellbore is oil based.
Description
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not Applicable.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates generally to the field of wellbore
instruments and well logging methods. More specifically, the
invention relates to systems and methods for estimating
permeability of subsurface rock formations using electrical
resistivity measuring instruments
2. Background Art
Well logging instruments are devices configured to move through a
wellbore drilled through subsurface rock formations. The devices
include one or more sensors and other devices that measure various
properties of the subsurface rock formations and/or perform certain
mechanical acts on the formations, such as drilling or percussively
obtaining samples of the rock formations, and withdrawing samples
of fluid naturally present in the pore spaces from the rock
formations. Measurements of the properties of the rock formations
made by the sensors may be recorded with respect to the instrument
axial position (depth) within the wellbore as the instrument is
moved along the wellbore. Such recording is referred to as a "well
log."
Well logging instruments can be conveyed along the wellbore by
extending and withdrawing an armored electrical cable ("wireline"),
wherein the instruments are coupled to the end of the wireline.
Such conveyance relies on gravity to move the instruments into the
wellbore. Extending and withdrawing the wireline may be performed
using a winch or similar spooling device known in the art. It is
also known in the art to use "logging while drilling" ("LWD")
instruments in certain circumstances. Such circumstances include
expensive drilling operations, where the time needed to suspend
drilling operations in order to make the wellbore accessible to
wireline instruments would make the cost of such access
prohibitive, and wellbores having a substantial lateral
displacement from the surface location of the well. Such
circumstances can also include large lateral displacement of the
wellbore particularly where long wellbore segments having high
inclination (deviation from vertical). In such cases, gravity is
not able to overcome friction between the instruments and the
wellbore wall, thus making wireline conveyance impracticable. LWD
instrumentation has proven technically and economically successful
under the appropriate conditions. LWD instrumentation has also
proven quite valuable for determining the position of the wellbore
with respect to certain types of rock formations during the
drilling of the wellbore, such that the wellbore may be drilled to
penetrate certain selected rock formations while avoiding others.
Such placement is facilitated by transmission of certain LWD
measurements to the surface during wellbore drilling operations. By
interpreting the measurements made during drilling, the wellbore
operator may make suitable adjustments to the wellbore trajectory
to maintain the wellbore within selected rock formations.
The use of LWD instruments has also made possible the determination
of the condition of certain permeable subsurface rock formations
prior to substantial displacement of the originally present fluid
disposed in the pore spaces of the rock formations by the liquid
phase of fluid used to drill the wellbore. As is known in the art,
typical wellbore drilling operations include pumping a liquid
having solid particles suspended therein through the pipe string
used to drill the wellbore. The suspension performs the functions
of maintaining a selected hydrostatic pressure in the wellbore to
prevent entry of fluids from the surrounding formations, to
maintain mechanical integrity of the wellbore, to cool and
lubricate the drill bit as it drills through the rock formations,
and to lift the drill cuttings to the surface for treatment and
disposal. In order to prevent entry into the wellbore of formation
fluids, the density of the drilling fluid is usually selected to
provide hydrostatic pressure somewhat greater than the fluid
pressure in the pore spaces of permeable subsurface rock
formations. A result of such conditions is that the liquid phase of
the drilling fluid is displaced into the pore spaces of the
formations, in a process called "invasion." At the time wireline
wellbore instruments are typically operated, the invasion process
has reached equilibrium, that is, a filter cake has deposited on
the wellbore wall adjacent to the permeable formations, and little
additional liquid phase of the drilling fluid enters the pore
spaces of the permeable formations. Wireline electrical resistivity
instruments typically include devices that have relatively short
axial resolution, and have lateral (radial) response generated
laterally proximate the wellbore. Such devices may be combined with
other devices that have successively greater lateral response and
larger (coarser) axial resolution. Measurements from such combined
devices may be processed to provide a result that is representative
of the electrical resistivity laterally deep enough into the
formation such that there is substantially no effect of the liquid
phase of the drilling fluid (the "uninvaded zone"). The results may
include an estimate of electrical resistivity of the formation
laterally proximate the wellbore such that the electrical
resistivity is representative of having some of the mobile original
or "native" fluid (i.e., the fluid present in the rock pore spaces
prior to any effects caused by drilling) moved by the liquid phase
of the drilling fluid (the "flushed zone").
When using LWD instrumentation, the foregoing types of measurements
may be made at a time so close to the initial penetration of the
rock formation by the drill bit, that relatively shallow invasion
has taken place. Thus, the relative lateral dimensions of the
flushed zone and the uninvaded zone may be different than those
measured at the time of wireline well logging. It is also known in
the art to move LWD instrumentation past previously drilled
formations one or more times during certain drilling operations.
For example, when reinserting the drill string into the wellbore
after a drill bit is changed, or when "reaming" or "washing" the
wellbore in order to improve its mechanical condition, the LWD
instruments may be moved past previously drilled formations and may
make measurements at such times. The drilling process also can have
periods of time where the LWD instrumentation is stationary in the
wellbore, e.g., such as when an additional section of drill pipe is
added to the drill string at the surface. The LWD instrumentation
may be configured to continue to make measurements of the formation
in front of the sensor during these stationary times. Such repeated
measurements and continuing stationary sensor measurements may
provide a basis to estimate permeability of the formations
penetrated by a wellbore.
SUMMARY OF THE INVENTION
One embodiment of the invention provides a method for determining
permeability of a subsurface formation includes measuring a
parameter related to fluid content of the formation at a first time
from within a wellbore penetrating the formation. A rate of entry
of fluid from the wellbore into the formation is determined from
the measurements of the parameter made at the first time. The
permeability is determined from the rate of entry.
Another embodiment of the invention provides a computer program
stored in a computer readable medium. The program includes logic
operable to cause a programmable computer to perform steps, which
include reading measurements of a parameter related to fluid
content of a subsurface rock formation made at a first time from
within a wellbore penetrating the formation. A rate of entry of
fluid from the wellbore into the formation is determined from the
measurements of the parameter made at the first time. A
permeability is determined from the rate of entry.
Other embodiments, aspects and advantages of the invention will be
apparent from the following description and the appended
claims.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an example of well logging instruments being conveyed
through a wellbore using a pipe string. In one example, the pipe
string is a "wired" pipe string.
FIG. 2 shows an example of a logging while drilling (LWD)
instrument that may be used in some examples.
FIG. 3 shows a flow chart of an example process according to the
invention.
FIG. 4 shows a graph of mud filtrate invasion with respect to time
at various drilling mud flow rates.
FIG. 5 shows a well log form graph comparing apparent fluid
invasion in permeable rock formations at initial penetration and at
a later time.
FIG. 6 shows a grid arrangement used in a reservoir simulation
according to one aspect of the invention.
FIG. 7 shows a time lapse comparison of fluid invasion where the
rock permeability is anisotropic.
FIG. 8 shows another example simulation grid arrangement.
FIG. 9 shows a programmable computer and various forms of computer
readable media.
DETAILED DESCRIPTION
In FIG. 1, a drilling rig 24 or similar lifting device moves a
conduit or pipe called a "pipe string" or "drill string" 20 within
a wellbore 18 that is being drilled through subsurface rock
formations, these formations being shown generally at 11. The drill
string 20 may be extended into the wellbore 18 by threadedly
coupling together end to end a number of segments ("joints") 22 of
drill pipe. In some examples, the drill string may be a so-called
"wired" pipe string. Wired drill pipe is structurally similar to
ordinary drill pipe and further includes at least one electrical
conductor or at least one optical fiber associated with each pipe
joint to act as a signal communication channel. Wired drill pipe
includes some form of signal coupling to communicate signals along
the channel between pipe joints when the pipe joints are coupled
end to end as shown in FIG. 1. See, as a non-limiting example, U.S.
Pat. No. 6,641,434 issued to Boyle et al. and assigned to the
assignee of the present invention for a description of a type of
wired drill pipe that can be used with the present invention. It
should be understood that the present invention may also be
operated with ordinary drill pipe that does not include such signal
communication channel.
The drill string 20 may include an assembly or "string" of wellbore
instruments at a lower end thereof, shown generally at 13 and which
may include "logging while drilling" ("LWD") instruments, which are
configurable to be used during drilling operations and which form
part of the pipe string itself. "Drilling operations" as used
herein means essentially any function related to using the drill
string in the wellbore, including without limitation actual
lengthening of the wellbore by operating a drill bit (explained
below), moving the drill string into or out of the wellbore, and
maintaining position of the drill string with drilling fluid
established or not.
Several of the components disposed proximate the drilling unit 24
may be used to operate part of the drilling and LWD system. These
components will be explained with respect to their uses in drilling
the wellbore to better enable understanding the invention. The
drill string 20 may be rotated by equipment on the rig (explained
below) in order to turn and axially urge a drill bit 17 into the
bottom of the wellbore 18 to increase its axial length (referred to
as "depth"). During drilling of the wellbore 18, a pump 32 lifts
drilling fluid ("drilling mud") 30 from a tank or pit 28 and
discharges the mud 30 under pressure through a standpipe 34 coupled
to a flexible conduit 35 or hose, through the top drive 26 and into
an interior passage (not shown separately in FIG. 1) inside the
drill string 20. The mud 30 exits the drill string 20 through
courses or nozzles (not shown separately) in the drill bit 17,
where it then cools and lubricates the drill bit and lifts drill
cuttings generated by the drill bit 17 to the Earth's surface.
During LWD well logging operations, the pump 32 may be operated to
provide fluid flow to rotate one or more turbines (not shown in
FIG. 1) in the LWD instrument string 13 to provide electrical
and/or hydraulic power to operate certain devices in the LWD
instrument string 13.
As the LWD instrument string 13 is moved along the wellbore 18 by
moving the drill string 20 as explained above, signals detected by
various sensing devices, non-limiting examples of which may include
a combination density/neutron porosity instrument 16, a gamma ray
sensor 14 and an electrical resistivity sensor assembly 10 are
selected to be included in a telemetry format for transmission to
the surface using a telemetry converter sub 12 for communication
along the signal channel (if a wired pipe string is used), and/or
by modulating flow of the drilling mud 30 using a mud flow
modulation valve (not shown separately) of any type known in the
art. At the surface, a telemetry transmitter 36A can be used to
wirelessly transmit signals from the drill string 20 (if wired) to
a receiver 36B. Thus, the drill string 20 (if wired) may be freely
moved, assembled, disassembled and rotated without the need to make
or break a wired electrical or optical signal connection. Signals
from the receiver 36B, which may be electrical and/or optical
signals, for example, may be conducted (such as by wire or cable)
to a recording unit 38 for decoding and interpretation using
techniques well known in the art. The decoded signals typically
correspond to the measurements made by one or more of the sensors
in the well logging instruments 10, 14, 16. Other sensors known in
the art include, without limitation, acoustic travel time or
velocity sensors, seismic sensors, neutron induced gamma
spectroscopy sensors and nuclear magnetic resonance sensors. It
should be understood that the transmitter 36A and receiver 36B may
be substituted by transceivers so that signal communication may
also be provided from the recording system 38 to the LWD instrument
string 13 or any component thereof. Preferably at least one of the
sensors in the LWD instrument string makes measurements related to
the fractional volume of pore space ("porosity") of the formations
11 adjacent to the wellbore 18.
The functions performed by the converter sub 12 may include
providing a mechanical coupling (explained below) between the pipe
string 20 (e.g., at the lowermost threaded connection) and an
uppermost connection on the well logging instrument string 13. The
converter sub 12 may also include one or more devices (explained
below) for producing electrical power to operate various parts of
the well logging instruments 13. Finally, the converter sub 12 may
include signal processing and recording devices (explained below
with reference to FIG. 4) for selecting particular signals from the
well logging instrument string 13 for transmission to the surface
using the communication channel in the pipe string 20 (if wired)
and recording signals in a suitable storage or recording device in
the converted sub 12. Signals transmitted from the surface may be
communicated through the communication channel in the drill string
20 (if wired) to the instrument string 13 through the various
devices in the power sub 12.
In addition, or in substitution of the foregoing, mud flow
modulation telemetry according to types well known in the art may
be used to communicate certain measurements to the surface. For
example, receiver 36B may include a pressure transducer (not shown
separately) for detecting the pressure of the mud 30 as it is
discharged from the pump 32. Changes in pressure caused by the
modulator (not shown separately) in the converter sub 12 may be
decoded and interpreted to correspond to certain measurements made
by the various sensors in the LWD instrument string 13.
It will be appreciated by those skilled in the art that in other
embodiments the top drive 26 may be substituted by a swivel, kelly,
kelly bushing and rotary table (none shown in FIG. 1) for rotating
the pipe string 20 while providing a pressure sealed passage
through the pipe string 20 for the mud 30. Accordingly, the
invention is not limited in scope to use with top drive drilling
systems.
A sensor associated with the top drive 26 (or swivel in kelly/kelly
bushing rotary drive systems) may be used to determine the
elevation of the top drive 26 over the drill floor of the rig at
any time. The top drive elevation may be combined with a record of
the lengths of all the components in the drill string 20, including
the pipe joints 22, converter sub 12 and the well logging
instruments 10, 14, 16 such that a record with respect to time of
the axial length (depth) of the wellbore 18 may be made. The axial
position of each sensor in each LWD instrument is known or is
determinable with respect to the lowermost face of the drill bit 17
or other positional reference along the drill string 20. Using such
position information, drill string length and the top drive
elevation, the axial position of each LWD sensor at any time may be
recorded, e.g., in the recording unit 38. The purpose for such time
indexed position record as it relates to the invention will be
explained in more detail below.
An example LWD resistivity instrument (e.g., shown at 10 in FIG. 1)
is shown in more detail in FIG. 2 to illustrate certain
measurements that can be used with a method according to the
invention. The instrument 10 shown in FIG. 2 may be the same as or
similar to one used to provide services under the mark GeoVISION,
which is a service mark commonly owned with the present invention.
The instrument 10 may include certain devices disposed within a
housing 10H, wherein the housing 10H is configured to be coupled
within the drill string (20 in FIG. 1). The devices can include,
for example, a toroidal electromagnetic transmitter 10A configured
to enable electromagnetic radiation therefrom to travel through the
wellbore (18 in FIG. 1) and through the formations (11 in FIG. 1).
Certain sensing devices on the instrument 10 are configured to
detect voltage drop and/or electromagnetically induced voltages
resulting from electromagnetic energy from the toroidal transmitter
10A. Such sensors may include button electrodes 10B, 10C, 10D
disposed at successively longer longitudinal distances along the
housing 10H from the position of the transmitter 10A. The sensors
may include a ring electrode 10E disposed at even greater
longitudinal distance from the transmitter 10A. In some
configurations, the drill bit 17 may be used as an electrode as
part of a voltage drop measuring circuit. In some examples a
pressure sensor 10F may be configured to measure fluid pressure in
an annular space between the instrument 10 and the wall of the
wellbore (18 in FIG. 1) for purposes to be explained further
below.
An aspect of the device shown in FIG. 2 and described in the
foregoing brochure is that the button electrodes 10B, 10C, 10D each
make a measurement corresponding to electrical resistivity at
successively greater lateral or radial displacement ("depth") from
the wellbore wall, and therefore respond differently for any
particular spatial distribution of electrical resistivity proximate
the wellbore wall. The spatial distribution of electrical
resistivity in a permeable formation proximate the wellbore wall is
related to the depth of "invasion" of mud filtrate into the
permeable rock formation, the difference between the resistivity of
the displaced, connate water and/or the fractional volume of
displaced hydrocarbon and the resistivity of the mud filtrate.
Another aspect of the instrument shown in FIG. 2 is that the
resistivity measurements made by the button electrodes 10B, 10C,
10D subtend a relatively small angular portion of the circumference
of the formations surrounding the wellbore, and thus may be
inferred to have measured the resistivity response along an
azimuthal direction corresponding to the particular rotational
orientation of the button electrodes at any time. Rotational
orientation may be defined as an angle subtended between a line
normal to the instrument longitudinal axis extending through one of
the button electrodes and a geodetic or other reference line, or
more succinctly, the rotational orientation of the button
electrodes with respect to the reference. During drilling and other
wellbore operations, certain sensors in the LWD instrument string
(13 in FIG. 1) may be used to determine the rotational orientation
of the button electrodes with respect to a selected geodetic
reference, for example, geomagnetic North, or gravitational
vertical. Such sensors and means for determining orientation are
well known in the art and need not be explained in further detail
herein. See, for example, U.S. Pat. No. 5,606,124 issued to Doyle
et al. and incorporated herein by reference for specific examples
of such sensors.
FIG. 2 also illustrates the principle of movement ("invasion") of
the liquid phase of the drilling mud ("mud filtrate") into a
permeable rock formation, e.g., 11A. For purposes of the present
example, the formation 11A may be assumed to be hydrocarbon
bearing, that is, the pore spaces of the formation 11A are at least
partially saturated with oil and/or gas in their undisturbed state.
Proximate the wellbore wall, a "filter cake" 11B consisting of
solid particles removed from suspension in the mud (30 in FIG. 1)
becomes disposed on the face of the permeable formation 11A by the
action of differential fluid pressure between the wellbore and the
formation. The separated liquid phase of the drilling mud (the mud
filtrate) displaces the native fluid originally present in the pore
spaces of the formation 11A. Depending on factors including: (i)
the volume of fluid that the mud loses before the filter cake 11B,
is fully developed and become substantially impermeable; (ii) the
fractional volume of pore space of the formation (called
"porosity") containing mobile fluid; and (iii) the fluid pressure
in the wellbore as compared to the fluid pressure in the rock
formation 11A, the mud filtrate will displace mobile fluid to an
approximate lateral distance (diameter of invasion) shown in FIG. 2
as d.sub.i. At greater lateral distances than the diameter of
invasion, d.sub.i, the undisturbed native fluid in the formation
pore spaces results in the formation having an undisturbed or
"true" electrical resistivity Rt. In the zone where mobile fluid
displacement by mud filtrate has occurred (generally at lateral
distances less than d.sub.i), the electrical resistivity of the
formation may be referred to as the "flushed zone resistivity" and
represented by Rxo.
Various computation programs are known in the art for determining
the foregoing three parameters (true resistivity, flushed zone
resistivity and diameter of invasion) from measurements made by
instruments such as the one shown in FIG. 2 and equivalent
instruments. Such programs typically require, as input, resistivity
measurements having a plurality of different "depths of
investigation", meaning spatially distributed responses, the
response for each sensor having a different lateral displacement
from the wellbore wall. For the instrument in FIG. 2, the
measurements used in the computation may include those from each of
the three button electrodes, possibly supplemented by measurements
from the bit 17 (as an electrode) and the ring electrode 10E.
One type of such computation program to determine Rxo, Rt and
d.sub.i from multiple depth of investigation resistivity
measurements is known as "inversion." Inversion may be described in
terms of its operation as generating an initial model of the
formation structure, including the three result parameters above,
namely Rxo, Rt and d.sub.i. An expected response of each sensor on
the instrument that would result from the initial model is then
generated. Such "forward" response calculation may be based on the
spatial distribution of the response field of each sensor and the
spatial distribution of electrical resistivity of the initial
model. The expected instrument response is then compared to the
actual measurements made by the instrument. Based on differences
between the expected response and the measurements, the initial
model may be adjusted (e.g., by changing any or all of the result
parameters), and the foregoing is repeated until differences
between the expected (forward calculated) responses and the
instrument measurements fall below a selected threshold. The
adjusted model at that time may be inferred to be the approximate
electrical resistivity structure of the subsurface. Such
resistivity structure may include the foregoing parameters Rt, Rxo
and d.sub.i.
LWD instruments in general, including the instrument shown in FIG.
2, make measurements that are indexed with respect to the time at
which each sensor is interrogated. Time may be measured by a clock
(not shown separately) in the instrument 10 that may be
synchronized with a reference clock, e.g., in the recording unit
(38 in FIG. 1) at times when the instrument 10 is in signal
communication therewith. Signal communication may take place using
wired drill pipe in some embodiments, or in other embodiments when
the instrument 10 is withdrawn from the wellbore (18 in FIG. 1) and
is electrically or optically connected to the recording unit (38 in
FIG. 1). The time indexed measurements may be recorded in a data
recording or storage device (not shown) in the instrument 10,
and/or may be transmitted to the Earth's surface using the
communication channel and/or mud flow modulation telemetry. In the
case of mud flow modulation data communication, or in still other
examples where sensor data are only recorded in the instrument 10,
the time indexed records may be later correlated to a time/depth
record made at the surface by making the time indexed record of the
elevation of the top drive (26 in FIG. 1) explained above and the
length of all the components of the drill string (20 in FIG. 1). In
combination, a record of the axial position (depth) of each sensor
on each LWD instrument with respect to time may be made.
In some examples, each of the resistivity sensors on the instrument
10 may move past a same axial position (e.g., formation 11A) a
plurality of times depending on the particular drilling operation
being performed at any time. A first movement (called a "pass") may
take place during the drilling of the wellbore, such that the
sensor makes a first pass thereafter. Later passes may correspond
to other drilling operations, such as withdrawing the instrument 10
from the wellbore, "backreaming" (rotating the pipe string while
pulling thereon), washing, circulating, inserting the drill string
into the wellbore, etc. Records of the measurements made by each
sensor (e.g., 10B, 10C, 10D, 10E, 10F) may be correlated to the
time/depth record such that particular sensor measurements may be
identified for each time a particular position in the well is
passed. The measurements made by each sensor may thereby be
correlated to the time after initial penetration of any particular
formation by the drill bit 17. Such time is typically presented in
well log format as a "time since drilled" or "time after bit" curve
alongside the particular measurement and/or computer results being
displayed in the well log.
By using the instrument shown in FIG. 2, or any similarly
configured electrical resistivity instrument, including, as will be
explained below, wireline instruments, it is also possible to index
the measurements made by the button electrodes 10B, 10C, 10D with
respect to the rotary orientation of the button electrodes at any
time. As will be further explained below, such rotationally indexed
measurements may be used to help estimate permeability anisotropy
of certain formations.
During drilling of the wellbore, there is frequently insufficient
time for filter cake 11B to settle onto the wellbore wall adjacent
permeable rock formations in sufficient amounts for the drilling
mud, the formation fluids and filter cake to reach equilibrium,
i.e., where substantially no additional mud filtrate permeates the
formation. Alternatively, equilibrium-thickness filter cake may
become dislodged by the continued action of the drill string (20 in
FIG. 1) and/or by erosion due to the flow of the drilling mud (30
in FIG. 1) and drilling tools at the bottom end thereof (including
the LWD instrument string 13). As a result, over time additional
mud filtrate invasion may occur and it may be possible to obtain
time lapse measurements, in particular from the electrodes on the
instrument shown in FIG. 2 Such time lapse measurements may then be
processed to determine, with respect to time, change(s) in the
depth of invasion (d.sub.i). As explained above, measurements made
by the various sensors in the LWD instrument string are typically
indexed with respect to the measurement time, and such time index
is associated with each measurement, thus making possible the
foregoing described time lapse measurements. Such time based change
in the invasion depth may be used along with other measurements
made by the LWD instrument string (such as those to calculate
fractional volume or rock pore space ("porosity")), to determine
the volume rate at which filtrate is entering the formation.
Examples of such measurements provided above with reference to FIG.
1 include density and neutron porosity. Determining porosity from
well log measurements is well known in the art and need not be
explained in further detail with reference to the present
invention.
The mud filtrate volume entry rate determined using time lapse
resistivity measurements may be used to estimate permeability of
the formation 11A. Referring briefly to FIG. 4, example curves
showing relative amounts of mud filtrate permeation through mud
cake with respect to time are illustrated for the cases of well
drilling using high mud flow, at curve 64, drilling or circulating
at low to moderate mud flow, at curve 66, and static conditions (no
mud flow), at curve 68. What may be inferred from FIG. 4 is that
particularly at high mud flow rates, the amount of filtrate loss
may be approximately linear with respect to time. Such relationship
may assist in estimating changing filtrate volume with respect to
time, (and therefore filtrate invasion rate) and thereby the
permeability of selected rock formations.
In one example, the mud filtrate invasion rate into any particular
formation can be estimated by calculating the total moved fluid
volume divided by the total time, Such rate may be calculated the
first time the LWD sensors pass by a formation of interest. The
total exposure time of the formation to the wellbore fluid may be
determined from the "time since drilled" record made in the LWD
instruments. Thus, in a first calculation, an volume of moved fluid
may be determined from the inversion explained above, and divided
by the time since drilled to obtain a rate of fluid entry. Such
procedure may be repeated for subsequent measurements and
inversions as long as the time of measurement since the formation
was drilled is determinable. In this example, an approximation for
the mud filtrate volume may be made by assuming that the mud
filtrate is only displacing hydrocarbons from the pore spaces of
the rock formation. Such assumption is useful because it is
primarily hydrocarbon bearing formations that are of economic
interest, and displacement of hydrocarbon by mud filtrate is
indicative of the likelihood that such formation will produce
hydrocarbon when the well is completed.
Moved hydrocarbon volume for each well log depth increment can be
calculated, for example, as the product .left
brkt-bot.(0.5*di-0.5*dh).sup.2*.pi.*phi*(Sxo-Sw)*depth
increment.right brkt-bot.
wherein d.sub.h represents the wellbore diameter, phi is the
porosity, and the quantities Sxo and Sw represent, respectively the
flushed zone water saturation and the undisturbed (native) water
saturation. The depth increment may be determined by calculating a
difference in depth between successive time-based well log data
samples (see the explanation above for how LWD data are recorded).
Alternatively, the depth increments may be calculated directly in
the recording unit (38 in FIG. 1) if wired drill pipe is used and
the measurements from the LWD instrument 10 are communicated to the
surface substantially in real time. Regardless of the method of
calculation, the depth increment in the above equation represents
the depth increment between successive measurements used in the
formula. The total moved fluid volume may be determined as the
integrated sum of the moved volumes over multiple depth increments.
The foregoing calculations may also be performed with reference to
bulk fluid volumes according to the expression: (0.5d.sub.i-0.5
d.sub.h)^2*.pi.*(BVWxo-BVW)*depth increment, with depth and
diameters in similar units as in the previous expressions. BVWxo
represents the bulk volume of water in the flushed zone and can be
determined by the expression (Rmf/Rxo).sup.(l/w) where Rmf
represents the resistivity of the mud filtrate, Rxo represents the
flushed zone resistivity and w=m=n. BVW represents bulk volume of
water in the uninvaded zone and can be determined by the expression
(Rw/Rt).sup.(l/w) where w=m=n.
The moved hydrocarbon fraction can be calculated using any
petrophysical volume solver software program. For example, the
inversion program used to calculate diameter of invasion and the
flushed (Rxo) and uninvaded zone (Rt) resistivities with the
GeoVISION service explained above also can compute an approximation
of the moved hydrocarbon volume. The initial fractional volume of
connate water (Sw) in the formation pore space prior to filtrate
invasion can be represented by a simplified form of the Archie
equation, e.g., the expression Sw=(F*Rw/Rt).sup.0.5, where Rw
represents the electrical resistivity of the connate water in the
rock pore spaces, and F represents the formation resistivity
factor. For simplicity it may be assumed that the Archie equation
parameters a=1 and m=n=2, which results in the above expression for
Sw. Rxo (the flushed zone electrical resistivity) is assumed to be
equal to Rt before substantial invasion has occurred. In practice,
it has been determined that if measurements of the resistivity of
the formation 11A are made relatively shortly after penetration by
the drill bit 17, the resistivity measurements made by an
instrument such as the one shown in FIG. 2 are capable of resolving
Rt using, for example, the described inversion procedure. The
fractional volume of water in the pore spaces in the "flushed" zone
(where all mobile fluid has been displaced by mud filtrate),
referred to as Sxo, is also determinable by a modified Archie
expression, e.g., the expression Sxo=(FRmf/Rxo).sup.0.5, where Rmf
represents the electrical resistivity of the mud filtrate. Rmf can
be measured from samples obtained at the surface. Rw may be
determined by extracting samples of formation connate water, or by
calculation (e.g., using the Archie expression) from an adjacent or
nearly adjacent formation that is inferred to be fully water
saturated. Such calculation can be made by the expression Ro=F*Rw,
wherein Ro is the electrical resistivity of a fully water saturated
porous rock formation and F is the same "resistivity formation
factor" referred to earlier. F may be determined using, for
example, using empirical relationships with respect to porosity.
One example of such relationship is F=aO.sup.-m, in which a and m
are constants and O represents the porosity. Porosity may be
obtained from certain of the LWD measurements as explained
above.
The generalized form of the Archie expressions described above for
the uninvaded zone and the flushed zone are, respectively:
Sw.sup.n=Rw/(O.sup.mRt); and Sxo.sup.n=Rmf/(O.sup.mRxo)
Rw and Rmf are fixed parameters that may be input into the above
described inversion, the button electrode resistivity measurements
at each depth increment are entered as data, and Rt and Rxo and
d.sub.i are solved by the inversion. Rt and Rxo may be used with
their corresponding measurements of fluid resistivity (Rw and Rmf)
to determine any change in the fractional volume of pore space
filled with water as between the uninvaded zone and the flushed
zone. By calculating water fractional pore space volume
(saturation) in the uninvaded zone, typically when the instrument
first measures the newly drilled formation, and subtracting the
fractional volume of water in the flushed zone, the result is the
fractional volume of moved hydrocarbons displaced by the mud
filtrate. The bulk volume of displaced or moved hydrocarbon is
reasonably assumed to be equal to the bulk volume of mud filtrate
invasion. Bulk volume may be determined from fractional volume by
multiplying fractional volumes by the porosity (determined, e.g.,
from other sensors in the LWD instrument string), and using the
depth increment explained above to calculate total rock volume. By
repeating the foregoing procedure each time the instrument moves
past the same axial position (formation) in the wellbore the total
volume of mud filtrate invaded into the formation may be determined
with respect to time. By determining filtrate invasion volume with
respect to time, a rate of infiltration may be determined. It is
also possible to determine fluid invasion volume using similar
sensor measurement techniques during periods of time when the drill
string is stationary in the wellbore (e.g., during addition of a
joint of drill pipe to or removal of a joint from the drill
string). As explained above, a fluid invasion volume may be
determined the first time and any individual subsequent time the
measurements are made using the time since drilled information
recorded by the LWD instruments, and such time may be used directly
to determine rate of invasion from the invasion volume determined
from the resistivity measurements.
Those skilled in the art will readily appreciate that corresponding
formulas and techniques may be applied in the case where the
drilling mud has hydrocarbon as the continuous liquid phase ("oil
based mud"), and as a result, the method of the invention is not
limited to use with water based drilling fluids.
It should also be clearly understood that subsequent sets of
measurements made at later times may be made using well logging
instruments conveyed on an armored electrical cable ("wireline"),
or coiled tubing, or any other type of conveyance. The method of
the invention is not limited to subsequent measurements being made
using drill string conveyed (LWD) instruments.
In one embodiment, the foregoing volume rate of filtrate invasion
may be combined with a pressure difference between the fluid
pressure in the formation 11A and the mud pressure in the wellbore
(determined, e.g., using the pressure sensor 10F) to estimate
formation permeability. Fluid pressure in the wellbore p may also
be determined by calculation using the formula p=.rho.gh, wherein
.rho. represents the drilling mud density, g represents
acceleration of gravity and h is the true vertical depth of the
particular formation.
FIG. 5 shows an example of the radii of invasion at the time of
initial drilling or penetration of the formation (curve 72) and at
a later time, such as during tripping, reaming or washing (curve
74) calculated using the foregoing inversion procedure. Effective
porosity of the formations is shown at curve 70. Separation between
curves 72 and 74 indicates that dynamic mud infiltration is taking
place into the permeable rock formations. Curves 72 and 74 show
that there is a moving fluid invasion "front" advancing laterally
into the formation with respect to increasing time since the
initial penetration of the formation by the drill bit (17 in FIG.
1).
"Spurt loss" may be characterized as mud filtrate invasion that
occurs in the first couple of minutes after a formation is
initially drilled by the bit, prior to build up of any effective
thickness of mud cake. It has been observed that the "spurt loss"
filtrate invasion rate can be considerably larger than the
equilibrium dynamic filtrate invasion rate. Therefore, one example
technique is to compute the mud filtrate invasion rate by
calculating the difference between the mud filtrate invasion volume
at the time of a subsequent (e.g., reaming or tripping) movement of
the LWD instrument past a selected formation and the initial
drilling thereof, divided by the total elapsed time between the
measurements made at each such time. The foregoing procedure can
minimize the influence of the spurt loss on the analysis. It is
contemplated that a greater number of LWD instrument passes over
time and corresponding measurements made in a selected rock
formation will provide even more reliable estimation(s) of
permeability because the determined filtrate invasion volume with
respect to time will correspond to the graphs in FIG. 4, and
thereby enable the user to better quantify the invasion volume and
invasion rate at any particular time during the invasion
process.
An additional procedure can be used to further refine the
calculation of the mud filtrate invasion rate using a reservoir
simulation software program. A series of grid cells around the
wellbore is initialized and the invasion process is modeled using
the reservoir simulation software program. One such program is sold
under the trademark ECLIPSE, which is a trademark commonly owned
with the present invention. Other reservoir simulation programs
capable of performing similar functions are known in the art. Such
reservoir simulation programs subdivide the volume of subsurface
rock formations into discrete, selectable volume "grid cells." By
using such simulation program, the mud filtrate invasion rate
calculated for each grid cell can be compared to the results of the
inversion analysis as explained above, e.g., using the GeoVISION
instrument's measurements. One advantage of such comparative method
is better quantification of the amount of time that any particular
section of the wellbore has been exposed to mud filtrate from the
time it was initially drilled to the time the specific measurements
were made. This elapsed time can be calculated by summing the time
beginning with the moment in time that the formation was initially
drilled until the point in time that the drill string is removed
from the wellbore, plus any amount of time spent in auxiliary
operations including "back reaming" (rotating the drill string
while pulling) and any time after the bit penetrates the particular
depth point for any other auxiliary operation. By determining the
total exposure time of the formation to the wellbore, it is
possible to run the simulation software to any desired number of
time increments for any selected cells in the simulation grid.
The ECLIPSE software or any equivalent numerical simulator that can
be used in near-wellbore modeling can then be operated to simulate
the invasion process. Imbibition relative permeability and
imbibition capillary pressure curves should be used where
available. In any case, the end-point relative permeability to oil
(permeability to oil corresponding to residual oil saturation [Sor]
conditions) should be altered to be consistent with the residual
oil saturation calculated in the petrophysical solver (from the Rxo
and Rt values calculated in the above-described inversion). This is
because the Sor calculated in the petrophysical solver is used to
calculate the amount of moved hydrocarbon as a fraction of unit
volume in order to estimate the mud filtrate invasion volume.
The reservoir simulation model should preferably be initialized
with extremely fine grids and small time increments. For example,
the grid cells near the wellbore can be about 2.5 mm in length and
the time increments about 0.0035 days (300 seconds). Such grid size
and time increments are intended to minimize any numerical
dispersion in the simulation results proximate the wellbore. At
greater lateral distances from the wellbore the grid cells can be
larger.
An example process for estimating permeability from LWD
measurements using a reservoir simulation program is shown in a
flow chart in FIG. 3. At 30, measurements from the GeoVISION or
similar LWD instrument such as described above may be allocated to
the rotary orientation at which they were made in order to exclude
unreliable measurements, and in some examples to enable determining
permeability anisotropy. At 32, measurements made, e.g., from the
ring electrode and button electrodes may be inverted to determine
Rt, d.sub.i and Rxo shortly after the drill bit has first
penetrated a particular formation. At 52, the results of such first
inversion include the foregoing parameters at the relevant time and
an estimate of invaded fluid volume. At 34, after the well logging
instrument has passed the formation a second time, the measurements
made may be used to once again invert for Rt, Rxo and d.sub.i. At
54, a new value of fluid invasion volume may be determined. At 36,
a fluid invasion rate may be estimated from the difference between
the prior two volume calculations and the elapsed time between the
measurements made for each inversion. At 56, the mud filtrate
invasion rate is determined using the foregoing volumes and elapsed
time. At 38, a reservoir simulation program such as the
aforementioned ECLIPSE program may be initialized to estimate flow
rate of mud filtrate into the formation. At 56, the simulator flow
rate is compared to the estimated flow rate. Values of permeability
used in the simulation may be adjusted, and the process repeated
until a simulation program filtrate invasion rate and the estimated
rate made from the repeated measurements substantially match.
At 40, measurement simulations and inversion using the reservoir
simulator may be performed using fine grid cell size and fine time
increments to estimate formation permeability anisotropy. In one
example, the measurements made by the instrument (10 in FIG. 2) may
be allocated according to rotary orientation such that differential
fluid volumes may be determined with respect to rotary orientation.
Such differential fluid volumes with respect to orientation may be
used alone or in conjunction with the reservoir simulation program
to estimate a maximum permeability direction and a minimum
permeability direction of a particular formation, with
corresponding maximum and minimum permeability, values. At 60, the
result of the foregoing is an estimate of permeability anisotropy.
At 42, the determined permeability and anisotropy if calculated may
be entered into a reservoir performance simulator (e.g., ECLIPSE or
the like) to estimate future production from a well or wells
penetrating the particular reservoir. At 62, a sensitivity analysis
may be performed to determine the relative effect of permeability
on reservoir performance as contrasted with other reservoir
parameters, such as pressure, water saturation, wellbore pressure,
etc.
The annular pressure while drilling sensor (10F in FIG. 2) may be
used in the instrument string can provide an accurate value for the
circulating pressure in the annulus while drilling ("bottom hole
pressure"). The numerical simulator is configured such that the
bottom hole pressure parameter is fixed and the simulator
calculates the corresponding filtrate invasion rate that is
required to satisfy the injectivity factor for each grid cell,
which is related to formation permeability and the pressure drop
between the wellbore and the particular formation. If the
calculated filtrate (injection) rate is the same as the invasion
rate as calculated using the diameters of invasion with respect to
time from the GeoVISION measurement inversions, then the
permeability estimated in the selected grid cell(s) may be inferred
to be a good estimation of actual formation permeability. The
permeability in the grid cells can be varied and the reservoir
simulation re-run until a good match is obtained between the
simulation filtrate invasion rates and the filtrate invasion rates
obtained by repeated measurement and inversion using the GeoVISION
measurements. The time increment at this point will define the
total volume injected whose corresponding invasion diameter will be
similar to the invasion diameter calculated in the GeoVISION
inversion for this ream pass. An alternative approach is to hold
the invasion rate constant and match the bottom hole pressure from
the simulator with the annular pressure sensor.
A first pass of the simulation program can be run without
accounting for the presence of mudcake. Since mudcake is present
(even during dynamic filtration of while-drilling), not accounting
for it will result in modeled invasion flow rates from the
simulator that may be higher than those obtained from the above
described resistivity inversion. Mudcake can be accounted for in
the first 2-3 cells from the wellbore. An initial mudcake
permeability should be derived from the drilling mud supplier or
publications describing test results of filter cake formation.
Thereafter, both the mudcake permeability and the formation
permeability can be varied so that the values (invasion flow rate
or bottom hole pressure) from the simulator program match the
values determined from the inversion processing. This would be
equivalent to the mudcake permeability during the static filtration
invasion phase. The mudcake permeability during the dynamic and
static invasion phases are substantially identical. The only thing
that is different is the mudcake thickness. In the dynamic phase
the mudcake would be thinner than in the static phase. Thinner
mudcake would allow a greater mud filtrate invasion into the
formation during the dynamic phase as predicted by Darcy's law.
Furthermore, there is greater pressure differential between the
wellbore and the formation in the dynamic phase resulting from the
ECD (equivalent circulating density) of the drilling fluid being
greater than its static density. Such higher differential pressure
results in higher invasion rate.
Care should be taken to identify, for each cell, which time
increment corresponds to the initial drilling pass, and which time
increment corresponds to any subsequent instrument pass. An example
of the simulation results is shown in FIG. 7. Permeable zones show
deeper invasion fronts than less permeable zones.
FIG. 6 shows an example of permeability estimation only accounting
for several gridcells at a time along the horizontal wellbore. This
is the position of the front at ream time. Note the importance of
including adjacent low permeability formations--a shale formation
is located next to the formation of interest.
Permeability anisotropy can be simulated in the ECLIPSE software as
shown in FIG. 8 and as explained above. In the example of FIG. 8
the ECLIPSE reservoir simulation model was initialized with a
permeability anisotropy ratio (k.sub.h/k.sub.v) of 1.63. The
permeability anisotropy ratio in the invasion diameters
(D.sub.ih/D.sub.iv) is 1.33, as can be seen in the result in FIG.
8. It is very important to ensure that grid cell dimensions are
equal in all dimensions X, Y and Z. This ensures that
transmissabilities between cells are only related to permeability
tensors and are not related to transmissibility changes at cell
surfaces.
Where gravity effects become important, the down invasion radius
may be slightly larger than the up invasion radius. The effects of
gravity and capillary pressure forces require the invasion process
to be modeled in a numerical simulator; the ratio of the invasion
radii calculated through resistivity inversions alone is not enough
to estimate the formation permeability anisotropy.
In another embodiment, the well logging instrument described with
reference to FIG. 2 may be substituted by a nuclear magnetic
resonance ("NMR") well logging instrument. One such instrument is
used to provide services under the mark proVISION, which service
mark is commonly owned with the present invention. As will be
appreciated by those skilled in the art, certain measurements made
by the foregoing instrument are related to the bulk volume of water
in the pore spaces of the rock formations. Such bulk volume of
water may change with respect to time in a manner essentially
identical to that explained with reference to FIG. 2. By measuring
the bulk volume of water at various times, a volume of hydrocarbon
displaced by mud filtrate may be determined, and such volume
displacement with respect to time may be used to estimate formation
permeability substantially as explained above. As used herein,
therefore, the term "parameter related to fluid content of the
formation" is intended to include electrical resistivity as well as
nuclear magnetic resonance properties, or any similar parameter
that can discriminate between hydrocarbon and water such that an
amount of native fluid moved by mud filtrate can be determined at
any time.
In another aspect, the invention relates to computer programs
stored in computer readable media. Referring to FIG. 9, the
foregoing process as explained with reference to FIGS. 1-8 can be
embodied in computer-readable code. The code can be stored on,
e.g., a computer readable medium, such as a floppy disk 164, CD-ROM
162 or a magnetic (or other type) hard drive 166 forming part of a
general purpose programmable computer. The computer, as known in
the art, includes a central processing unit 150, a user input
device such as a keyboard 154 and a user display 152 such as a flat
panel LCD display or cathode ray tube display. According to this
aspect of the invention, the computer readable medium includes
logic operable to cause the computer to execute acts as set forth
above and explained with respect to the previous figures.
Methods according to the invention may provide improved estimates
of permeability of subsurface rock formations prior to actual fluid
sample taking therefrom or flow testing thereof. Accordingly,
methods according to the invention may reduce the risk of testing
formations that are unlikely to be productive of hydrocarbons, and
may provide better results when used with reservoir simulation
programs to estimate future reservoir productivity.
While the invention has been described with respect to a limited
number of embodiments, those skilled in the art, having benefit of
this disclosure, will appreciate that other embodiments can be
devised which do not depart from the scope of the invention as
disclosed herein. Accordingly, the scope of the invention should be
limited only by the attached claims.
* * * * *